This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Separate the combined inequality into two individual inequalities. The given inequality is -1 (5-2x)/(3) < 2x-1 This can be split into two inequalities: 1) -1 (5-2x)/(3) 2) (5-2x)/(3) < 2x-1 Step 2: Solve the first inequality. -1 (5-2x)/(3) Multiply both sides by 3: -1 × 3 5-2x -3 5-2x Subtract 5 from both sides: -3 - 5 -2x -8 -2x Divide both sides by -2. Remember to reverse the inequality sign when dividing by a negative number: (-8)/(-2) x 4 x So, x 4. Step 3: Solve the second inequality. (5-2x)/(3) < 2x-1 Multiply both sides by 3: 5-2x < 3(2x-1) 5-2x < 6x-3 Add 2x to both sides: 5 < 6x + 2x - 3 5 < 8x - 3 Add 3 to both sides: 5 + 3 < 8x 8 < 8x Divide both sides by 8: (8)/(8) < x 1 < x So, x > 1. Step 4: Combine the solutions from both inequalities. From Step 2, we have x 4. From Step 3, we have x > 1. Combining these two, we get the combined inequality: 1 < x 4 The final answer is 1 < x 4. Send me the next one 📸